ACR X EQUIP PROB FMS APCH COUPLER COMPASS MADE APCH TO WRONG RWY HAD NMAC LTSS WITH ACR Y. SYS ERROR.

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I WAS WORKING LCL CTL AND HAD PUT ACR X INTO POS TO HOLD ON RWY 9L PENDING THE ARR OF ACR Y ON RWY 9R. THE VISIBILITY WAS ALMOST NIL FROM THE TWR SO WE WERE USING THE ASDE. I CLRED ACR X FOR TKOF. IMMEDIATELY ACR X ADVISED THAT AN ACFT HAD OVERFLOWN HIM. ACR Y THEN ADVISED HE WAS GOING MISSED APCH. I THEN CANCELED ACR X TKOF CLRNC. SUPPLEMENTAL INFO FROM ACN 262158: ACR X POS AND HOLD ATL RWY 9L FOR 1 MIN WAITING FOR TKOF CLRNC. AN ACR Y MD80 FLEW RIGHT OVER US AT 50-100 FT WHILE WE SAT IN POS. ONLY A FEW SECONDS AFTER THE TWR CLRED US FOR TKOF. WE BEGAN OUR ROLL AND QUESTIONED THE ACFT FLYING OVERHEAD AT THE SAME TIME ATL TWR TOLD US TO ABORT. WE DID A VERY LOW SPD ABORT AND TAXIED BACK FOR ANOTHER TKOF. SECOND TKOF WAS UNEVENTFUL. ABORT WAS AT 30-40 KTS. SUPPLEMENTAL INFO FROM ACN 262397: CLRED INTO POS AND HOLD RWY 9L. WHILE WAITING FOR TKOF CLRNC AN MD80 CAME OUT OF THE CLOUDS (100 FT) AND FLEW DIRECTLY OVER US. (ACR Y HAD BEEN CLRED 9R APCH AND LNDG.) TWR; NOT SEEING ACR Y DUE TO TWR CAB IN CLOUDS; CLRED US FOR TKOF. ROLL STARTED AS WE QUESTIONED TWR ON THE OVERFLY. AT THAT TIME ACR Y CALLED THEY WERE GOING AROUND. TWR CALLED FOR US TO ABORT TKOF AND WE COMPLIED. SUPPLEMENTAL INFO FROM ACN 262402: AT THE START OF THE FLT AT LGA WE WERE ADVISED THAT A PREVIOUS COMPASS WRITE UP HAD BEEN FIXED BY REPLACING THE #1 COMPASS INDICATOR. ENRTE WE USED HDG SELECT ON THE AUTOPLT AND EVERYTHING SEEMED NORMAL. ON VECTORS TO THE 9R ILS AT ATL I COUPLED THE AUTOPLT TO THE ILS. ON CAPTURING THE ILS LOC THE AUTOPLT SEEMED A LITTLE SLUGGISH TO RESPOND AS WE PROCEEDED ON THE ILS. AT APPROX 500 FT AGL IT WAS SLIGHTLY TO THE R OF THE LOC AND STARTED TO CORRECT BACK TO THE L; WENT THROUGH THE LOC WITH A 15 DEG CORRECTION TO THE L. THE FLT DIRECTOR COMMAND BARS WERE SHOWING A SLIGHT CORRECTION TO THE R BUT THE AUTOPLT WAS NOT RESPONDING. I DISCONNECTED THE AUTOPLT FOR A MISSED APCH; STARTED CORRECTING TO THE R; AT THAT TIME WE BROKE OUT AT APPROX 1350 FT MSL. LINED UP FOR RWY 9L AND CONTINUED THE MISSED APCH PROC. ALL THIS OCCURRED SIMULTANEOUSLY. WE TOOK VECTORS FOR A SECOND APCH WHICH WAS FLOWN MANUALLY. AT APPROX 1250 FT MSL THE FO CALLED 'APCH LIGHTS IN SIGHT.' WHEN I LOOKED OUTSIDE I COULD NOT SEE ANYTHING SO THEN EXECUTED A MISSED APCH. WE DISCUSSED THE SIT AND DECIDED ON MAKING A MONITORED APCH WHICH WAS COMPLETED SUCCESSFULLY. AFTER LNDG THE PROB WAS RPTED TO MAINT. WE FOUND THE SAME PROB HAD BEEN RPTED ON PREVIOUSLY AND THE ROLL COMPUTER HAD BEEN REPLACED AND SIGNED OFF AS OP CHK OK. ON THE FIRST MISSED APCH I DID NOTICE AN ACFT SITTING ON RWY 9L AND ASSUMED IT WAS HOLDING IN POS. SINCE WRITING THE ABOVE; I HAVE FOUND OUT THAT IT HAD BEEN CLRED FOR TKOF; WHICH PRESENTS ANOTHER PROB.